Optimal Power Flow in Stand-Alone DC Microgrids

Abstract

Abstract-Direct-current microgrids (DC-MGs) can operate in either grid-connected or stand-alone mode. In particular, stand-alone DC-MG has many distinct applications. However, the optimal power flow problem of a stand-alone DC-MG is inherently non-convex. In this paper, the optimal power flow (OPF) problem of DC-MG is investigated considering convex relaxation based on second-order cone programming (SOCP). Mild assumptions are proposed to guarantee the exactness of relaxation, which only require uniform nodal voltage upper bounds and positive network loss. Furthermore, it is revealed that the exactness of SOCP relaxation of DC-MGs does not rely on either topology or operating mode of DC-MGs, and an optimal solution must be unique if it exists. If line constraints are considered, the exactness of SOCP relaxation may not hold. In this regard, two heuristic methods are proposed to give approximate solutions. Simulations are conducted to confirm the theoretic results.

Resilience Control of DC Shipboard Power Systems

“…Remark 2: As indicated in [22], the exactness of the convex relaxation of OPF in DC networks is independent of network topologies. Later in Section IV, we will further show that this result holds true for the SPSs considered in this paper.…”

“…By removing the rank constraint (10j), the non-convex SE1 is transformed to a convex MISOCP problem (named as SR1): SR1 is exact, provided that its every optimal solution satisfies the rank constraint (10j). In order to ensure the exactness of convex relaxation when the line constraint (10k) is inactive, throughout the rest of this paper, we make the following assumptions [22].…”

“…Thus, SR1 is illconditioned as (10a) needs the subtractions of δ i,ij and W ij , which may cause numerical instability. Such subtractions, however, can be avoided by using a branch flow formulation [22], so that the numerical stability is improved. To this end, we define z ij := 1/y ij and adopt alternative variables P and l. Then SR1 can be converted into a branch flow model via the mapping g : (v, δ, W ) → (v , δ , P, l) defined by: 14) where P ij denotes the power flow through line i → j, and l ij denotes the magnitude square of the current through line i → j.…”

“…In [21], a second-order cone program (SOCP) was first suggested to exactly relax the OPF problem in grid-connected DC distribution networks, with strict proofs and comprehensive discussions. It laid the foundation for solving optimal power flow (OPF) problems in DC distribution networks, and was further extended in [22] to a broader class of DC networks, including stand-alone DC microgrids. However, discrete operations, such as line switching and re-sectionalization, have not yet been considered in both works.…”

Decentralized DC Microgrid Monitoring and Optimization via Primary Control Perturbations

“…Motivated by the shortcomings of the above approaches, we propose a decentralized dual-layer control architecture for autonomous DC MGs in which each primary controller locally acquires the information required for the operation of the upper layer and determines the updated primary control references without the support of external communication enabler. To support the majority of applications, the upper control layer requires information about: i) the generation capacities of the dispatchable DERs, ii) the demands of the loads, and iii) the conductance matrix of the distribution network [17], [19]. This information can be inferred from local voltage observations, since the bus voltages are functionally related to the MG parameters through a non-linear model.…”